Christopher Columbus "prediction"

a From Liu and Fiala (1992). Magnitudes are indicated in parentheses. b Private communication to Stephenson and Clark (1978, pp. 30-31).

a From Liu and Fiala (1992). Magnitudes are indicated in parentheses. b Private communication to Stephenson and Clark (1978, pp. 30-31).

ent solar diameter was considered to have a width of 12 "points," each of which was divisible into 60 "minutes" and each "minute" again divisible into 60 "seconds." The "magnitude" in this context was the width of the eclipsed portion in these units (North 1988, p. 99); North notes that magnitudes were sometimes stipulated in area units as well). Modern techniques for computing times and eclipse magnitudes and for calculating eclipse maps are described in the Explanatory Supplement to the Astronomical Ephemeris and the Astronomical Ephemeris and Nautical Almanac (London: HMSO), 1961, among other sources. Link (1969) delineates the geometric details of lunar eclipses, both ancient and modern. Computer software is readily available to provide detailed images of the appearance of eclipses during various phases. The Canon of Lunar Eclipses of Liu and Fiala (1992) has companion software by Liu and Eagle that demonstrates both the appearance and the visibility of any of the lunar eclipses in the interval 1500 b.c. to 3000 a.d. anywhere on Earth.

Ancient eclipses have been and still are valuable to study for many reasons. First, the locations and times of ancient eclipses provided checks on theories of the motion of the Moon and Sun, in antiquity, for Hipparchos and Ptolemy (see the next section on lunar occultations); second, these data today provide information about the rate of change of the Earth's rotation (see §4.5 and Stephenson 1997 among other sources12); third, the size and shape of the solar corona

12 See also Newton 1974, p. 100; Muller and Stephenson 1975:

Stephenson and Clark 1978; Stephenson and Morrison 1984; Stephenson and Houlden 1986.

provide an indication of solar activity (see §5.3.1, on sunspots and sunspot cycles), and fourth, the magnitude of the eclipse provides data on the size of the solar photosphere (see §5.8.1, on eclipsing variable stars). The use of lunar eclipses to study the averaged volcanic aerosol of the stratosphere was suggested by Keen (1983).

The earliest series of recordings of eclipse observations appear to be on oracle-bones from a site near An-Yang called the "Wastes of Yin" in China (Needham 1981, p. 197; Stephenson and Houlden 1986, p. xii). The records, from the Shang dynasty (~1550-1045 b.c.) include six lunar eclipses in an early series and six solar eclipses dated three generations later. The precise dates are dependent on general Shang dynasty chronology (see § and Tables 10.1,10.5). A late Shang record bears the inscription "three flames ate up the sun, and a great star was visible." The "flames" may refer to the plume-like structure of the solar corona. As we discuss in §10, eclipses were important in China, but our records of Chinese observations of them are incomplete: Pang et al. (1988) note that the paucity of records from the Xia, Shang, and western Zhou dynasties must be due, at least in part, to the destruction of older records by the first emperor of China, Shi Huang Di (246-210 b.c.). Many eclipse records were made during the subsequent dynasties, and these are now proving invaluable in the determination of the rates of change of the Earth's rotation and the Moon's mean motion. A partial eclipse may be useful for this purpose too, if some special circumstance, such as visibility at sunrise or sunset, indicates the time of day. As recorded in The History of the Northern Wei Kingdom on a date in the first year of the reign of a King Chu, the Sun rose while in eclipse. Pang et al. (1988) date this eclipse to Nov. 13, 532 a.d.

One of the most interesting as well as potentially useful records is that of the day with the "double dawn" (Pang et al. 1988). This record is from the time of the Eastern Zhou dynasty (771-221 b.c.) and is found in the reconstruction of the Bamboo Annals (Zhu Shu Ji Nian), the original of which ends in the 20th year of the reign of King Hsiang (~299 b.c.), with whom they were buried. The record states that the day dawned twice during the 1st year of the reign of a Western Zhou king named Yi at a place called Zheng (109°8E, 34°5N), in the present Shaanxi Province, 27 km west of the Hua mountain range (Chang 1981), which rises several degrees above the true eastern horizon from that site. Pang et al. analyzed all eclipses between the likely dates for the first year of King Yi's reign (which they place in the range 966-895 b.c.)13 and concluded that an annular eclipse of April 21, 899 b.c., is the only one that fits the data. The description of the event is satisfied by the interruption of a normal dawn by the onset of 2nd contact, ~05:30 local time, when the Sun would have been less than 1° below the apparent (mountain) horizon, but already above the true horizon. At that time, the light would have decreased by thousands of times (the magnitude of the eclipse would have been 0.95) until 3rd contact, ~3 minutes later. Subsequently, a normal dawn would have appeared to return. Their analysis indicates that the accumulated clock error, AT, in the Earth's rotation over the nearly 2700y interval (to Jan 1,1800, taken as 0 by Pang et al.) is 5h48m ± 500s, in order to have the eclipse begin just east of Zheng. The eclipse track presented by Pang et al. (1988, Figure 3, p. 845) seems to coincide with that of Oppolzer (1887/1962), whose work assumed empirical corrections for what we now call AT; Pang et al. conclude that AT = 5h48m, but give few details of how they arrived at this value. Stephenson and Houlden (1986, p. 74) disagree on the track of the eclipse, however, and effectively disagree that the double dawn eclipse occurred on this date. They computed a value of AT of 6h59.m1 for this particular eclipse; their track, if accurate, indicates that the eclipse would have been invisible over mainland China, commencing at dawn on the western side of the Korean peninsula and proceeding northeastward across the Sea of Japan, longitudinally bisecting the island of Honshu. The track shifts produced by Stephenson and Houlden (1986) are based on several telescopic timings of lunar occultations (see §5.3.3), Arab timings of lunar and solar eclipses, medieval observations of eclipses, and Babylonian timings of lunar eclipses. Finally, Stephenson (1997, p. 220) expresses doubt that the event refers to an eclipse at all, because the term shih is not used in the description (see §10).

The work of Pang et al. (1988) suggests a value for the Earth's rotational acceleration, 1/2 e < -37 s/century2 (refer to §4.5 for definitions of secular variation and the affect on

13 According to Tchang (1905/1967, p. 36), King Yi began his reign in 894 b.c. This is according to traditional chronology that assigns 53 years to the reign of King Yi and his son, who is known to have been removed from the throne in 841 b.c., the first fully agreed date of Chinese history. Therefore, Pang's dates appear unlikely.

the observed time of eclipses and other phenomena). This result is not inconsistent with the results of analysis by Huber (1986) of Babylonian (lunar) eclipse records, —34 s/ century2. Of course, a consistent value for the acceleration of the Moon's motion is necessary as well. Stephenson and Houlden (1986) used for their extensive Far East eclipse track calculations a value of n = -26 arc x sec/century2, and for AT the following expression14 for years prior to 948 a.d.: AT = 1830 - 40.5 x T + 46.5 x T2. The coefficient of T2 is the equivalent of e = -93 s/century2. Work by Stephenson and Morrison (1980) yielded a similar relation, whereas the simple fitting of the parabola AT = 32.5 x T2 was derived from an analysis of Babylonian eclipse observations by Morrison and Stephenson (1982).

Ptolemy himself made use of ancient eclipse observations. For study of the motion of the Moon, he recognized the importance of lunar over solar eclipse records because the latter phenomenon is strongly dependent on the position of the observer, but the former is visible wherever the eclipsed Moon is above the horizon:

Whereas in the case of lunar eclipses there is no such variation due to parallax, since the observer's position is not a contributory cause to what happens at lunar eclipse. For the moon's light is at all times caused by the illumination from the sun. Thus when it is diametrically opposite to the sun, it normally appears to us lighted over its whole surface, since the whole of its illuminated hemisphere is turned toward us as well at that time. However, when its position at opposition is such that it is immersed in the earth's shadow-cone (which revolves with the same speed of the sun but opposite it), then the moon loses the light over a part of its surface corresponding to the amount of its immersion, as the earth obstructs its illumination from the sun. Hence it appears to be eclipsed for all parts of the earth alike, both in size [of the eclipse] and the length of the intervals [of the various phases]. (Toomer 1984, p. 174)

This passage sounds remarkably modern in tone and is essentially correct in all details, if we allow that the sun "revolves" about the Earth as referring to apparent motion only. The important consequence is that the Moon's ecliptic longitude and latitude are known precisely at the time of a lunar eclipse. This is the case even though the circumstances of the eclipse do not vary across a broad range of terrestrial longitudes and the exact time of night is not usually recorded. There are historical lunar eclipses for which useful time information exists, nevertheless. The earliest lunar eclipse entry in Ptolemy's list was that seen in Alexandria in the year 546 of the Nabonassar era, on the 27/28 day of the Egyptian month Phamenoth, from the 8th to the 10th hour (reckoned from sunset). It reached greatest magnitude (~0.5) at 21/2 seasonal hours after midnight. Ptolemy provides the records of four lunar eclipses (see Table 5.2), and these are useful in providing information on the local dates that he used (year of the reign of Hadrian and months and days in the Egyptian calendar; see Schove 1984, p. 25; §7.3 for further details).

A series of lunar eclipses that is remarkable for detailed timing information is included in the eclipse records com

14 For years between 948 and 1600 a.d., they used AT = 22.5 x T2; after 1600 a.d., AT was taken from tables of averages over five-year intervals by Stephenson and Morrison (1984).

piled by Ibn Iunis (d. 1009). For example, an eclipse was calculated and subsequently observed in Baghdad (44°24'E, 33°20'N) in 927 a.d. by Ali ibn Amajur and his son. The altitude of Sirius at the start (31°, "in the East"), and the rotation of the celestial sphere from sunset until onset of the eclipse (1481/3°) are specified. The latter is equivalent to 9h52m equal hours or 10 seasonal hours. According to Liu and Fiala (1992), the beginning of the partial (umbral) phase (72) should have been 01:11 UT on Sept. 14, maximum eclipse at 02:00 UT, and the end of partial phase (75) at 02:50 UT. We can reasonably ignore the penumbral start (7i) and end (T6) because these are difficult to discern with the eye alone. The longitude correction to local mean solar time is +2h96 = +02h 58m; adding this to T2, 01:11, we obtain 04:09 local mean time (LMT), or ~10h from the previous sunset. The position of Sirius (Table 3.1) can be precessed backward to get its position in 927 a.d. We compute the approximate equatorial coordinates: a = 05h57m5 and 8 = -15°35. From these, we compute the eastern hour angle of Sirius when it had an altitude of 31°: H = -34°93 = -02h20m, by means of (2.5). Thus, the local sidereal time is H + a « 03h38m. With a© ~ 12h, near the September equinox, H© ~ -08:22. This is ~02:22 before sunrise. According to the software progam Redshift, sunrise is at 05:47 on Sept. 14, and the Sun's right ascension is about 11h42m. These values give a solar hour angle of -08:04, or 02:14 before sunrise. Redshift also gives a time of sunset of 18:06 at Baghdad on Sept. 13. From this moment to the onset of the umbral eclipse is 10:03, a reasonable approximation to the time recorded by Ali ibn Amajur. The same program indicates Sirius to be ~32° above the horizon at the onset of the umbral phase of the eclipse; so the reported data are consistent.

Because the observation of a solar eclipse is so dependent on the location of the observer—in longitude as well as in latitude—all records have implicit time information; but all historical records are subject to distortion and to copyist error, especially if they represent recollection long after the event. In a review of the degree of reliability15 of ancient eclipse observations, Muller and Stephenson (1989) conclude that only four early solar eclipse records can be considered of the superior class "A" reliability:

• Total solar eclipse of 7 July 709 b.c., at Chu Fu, China

• Total solar eclipse of 26 Sept. 322 b.c., at Babylon

• Total solar eclipse of 4 March 181 b.c., at Ch'ang An,


• Total solar eclipse of 15 April 136 b.c., at Babylon

The records of the eclipse of 136 b.c. were evaluated by Stephenson and Clark (1978) as the most accurate before the invention of the telescope. Two separate records were found among the clay tablets of the astronomical diaries of Babylon, and these provided precise locations of the Sun and several planets in the sky during totality. On the basis of planet positions and the date of nearby eclipses, Huber was able to determine the date of the eclipse. In addition, a

"retrocalculation" by Mitchell (1989/90, p. 10) of the date of a lunar eclipse that occurred 14 days prior to the solar eclipse is also in agreement with the data recorded on one of the tablets.

Mitchell (1989-1990, p. 10) finds that values of the acceleration in the range 30-34 seconds/century2, or, roughly, the value 32.5, fit the most reliable data from Chinese and Babylonian records over the interval ~700 b.c. to ~135 b.c.; however, the complete details of the process are not clear. As we noted in §4.5, Stephenson and Morrison's (1995) preferred solution is 31.0 (±0.9) for the coefficient of i2, but make use of cubic splines to fit the data because they find evidence of additional terms (both periodic and secular) for the Earth's rotational acceleration.

A dramatic illustration of the effect of the accelerations on the timings of ancient eclipses was provided by Stephenson for Misner Thorne, and Wheeler (1973, p. 25), which shows that the uncorrected path of an eclipse predicted for 14 January 484 a.d., should begin at sunrise in the Atlantic ocean, just off the coast of Spain at a latitude ~40° (Figure 4.13). In fact, a record was made of the eclipse beginning in western Greece at about the same latitude but very close to 30° east of the predicted path of totality. This implies that the eclipse occurred two hours later than predicted. Because the Sun moves 30° in two hours = 7200 seconds, the difference in longitude implies a value:

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